Exploratory Analysis: FPCA for PFT Needleleaf Evergreen with disturbances between 2015 and 2040

Patches which face a disturbance between the years 2015 and 2040 are the basis for this analysis. As a first step in the exploratory analysis, the data is represented as functions by means of a b-spline basis equivalently as for PFT Tundra, i.e. b-splines of order 6, penalizing the third derivative with a penalization parameter \(\lambda = 1\).

Basis Representation - Needleleaf Evergreen

Figure 1 shows the chosen basis representation for Needleleaf Evergreen.

Figure 1: Smoothed basis representation for PFT Needleleaf Evergreen and all four scenarios.
Figure 1: Smoothed basis representation for PFT Needleleaf Evergreen and all four scenarios.

Principal Component Analysis - Needleleaf Evergreen

To further analyze the data, a FPCA is run for each of the four scenarios and each of the five PFTs separately. Again, let’s take a look at the two principal components for each scenario of PFT Needleleaf Evergreen. Figure 2 shows the principal components.

Figure 2: First two principal components for each scenario for PFT Needleleaf Evergreen
Figure 2: First two principal components for each scenario for PFT Needleleaf Evergreen

For Tundra, we could see huge differences between the Control scenario and the climate scenario. Here however, the principal components for all four scenarios are pretty similar and all reflect the same patterns: high values in the first PC stand for much higher values of above ground carbon than the mean after the 10 first years of the considered time span and vice versa for low values. The second principal component mainly reflects peaks in the last third of the study period.

With VARIMAX rotation

For a better understanding and an easier interpretation of the principal components, a VARIMAX rotation is applied. This rotation algorithm may reveal more meaningful components of variation in the data (Ramsay et al. (2009)).

Figure 3 shows the VARIMAX rotated first and second principal components for each scenario.

Figure 3: First two principal components for each scenario for PFT Needleleaf Evergreen with VARIMAX rotation.
Figure 3: First two principal components for each scenario for PFT Needleleaf Evergreen with VARIMAX rotation.

In this case, the VARIMAX rotation does not substantially increase the interpretability, since the first two principal components are hardly changed. Thus, a rotation might be unnecessary.

Cluster detection: PC1 vs. PC2 - Needleleaf Evergreen

In order to detect possible clusters in the data, i.e. the share of above ground carbon may behave in similar ways for several grid points, the two first principal components are plotted against each other for all considered cases: unrotated (Figure 4) and VARIMAX rotated (Figure 5). The color reflects a rough classifying into regions, here continents.

Figure 4: First principal component vs. second principal component for each scenario for PFT Needleleaf Evergreen.
Figure 4: First principal component vs. second principal component for each scenario for PFT Needleleaf Evergreen.

In Figure 4, a light clustering pattern is visible, especially for the more drastic scenarios. The three warming scenarios tend to follow a similar pattern. For the control scenario, the data is more scattered.

Figure 5: First VARIMAX rotated component vs. second VARIMAX rotated component for each scenario for PFT Needleleaf Evergreen
Figure 5: First VARIMAX rotated component vs. second VARIMAX rotated component for each scenario for PFT Needleleaf Evergreen

Rotation does not lead to a substantial difference in PC scores for Needleleaf Evergreen. This was already indicated in Figure 3 as the PCs hardly change in comparison to the unrotated ones.

Spatial Distribution visualized in world maps

In order to get a better understanding of the spatial component of the data, Figure 6 shows how the portion of above ground carbon from year 0 to 100 after disturbance develop in each grid cell (patch 1).

Figure 6: Spatial distribution of the portion of above ground carbon after distrubance for each scenario for PFT Needleleaf Evergreen.
Figure 6: Spatial distribution of the portion of above ground carbon after distrubance for each scenario for PFT Needleleaf Evergreen.

We can clearly see major differences between the scenarios and the considered regions. The more drastic the warming scenario, the less Needleleaf Evergreen is present. This pattern is possibly due to a higher share of temperate broadleaf in warmer scenarios.